Showing papers on "AdS/CFT correspondence published in 2011"

Quasinormal modes of black holes: From astrophysics to string theory

Abstract: Perturbations of black holes, initially considered in the context of possible observations of astrophysical effects, have been studied for the past 10 years in string theory, brane-world models, and quantum gravity. Through the famous gauge/gravity duality, proper oscillations of perturbed black holes, called quasinormal modes, allow for the description of the hydrodynamic regime in the dual finite temperature field theory at strong coupling, which can be used to predict the behavior of quark-gluon plasmas in the nonperturbative regime. On the other hand, the brane-world scenarios assume the existence of extra dimensions in nature, so that multidimensional black holes can be formed in a laboratory experiment. All this stimulated active research in the field of perturbations of higher-dimensional black holes and branes during recent years. In this review recent achievements on various aspects of black hole perturbations are discussed such as decoupling of variables in the perturbation equations, quasinormal modes (with special emphasis on various numerical and analytical methods of calculations), late-time tails, gravitational stability, anti--de Sitter/conformal field theory interpretation of quasinormal modes, and holographic superconductors. We also touch on state-of-the-art observational possibilities for detecting quasinormal modes of black holes.

Holographic c-theorems in arbitrary dimensions

Abstract: We re-examine holographic versions of the c-theorem and entanglement entropy in the context of higher curvature gravity and the AdS/CFT correspondence. We select the gravity theories by tuning the gravitational couplings to eliminate non-unitary operators in the boundary theory and demonstrate that all of these theories obey a holographic c-theorem. In cases where the dual CFT is even-dimensional, we show that the quantity that flow is the central charge associated with the A-type trace anomaly. Here, unlike in conventional holographic constructions with Einstein gravity, we are able to distinguish this quantity from other central charges or the leading coefficient in the entropy density of a thermal bath. In general, we are also able to identify this quantity with the coefficient of a universal contribution to the entanglement entropy in a particular construction. Our results suggest that these coefficients appearing in entanglement entropy play the role of central charges in odd-dimensional CFT's. We conjecture a new c-theorem on the space of odd-dimensional field theories, which extends Cardy's proposal for even dimensions. Beyond holography, we were able to show that for any even-dimensional CFT, the universal coefficient appearing the entanglement entropy which we calculate is precisely the A-type central charge.

Emergent quantum criticality, Fermi surfaces, and AdS 2

Abstract: Gravity solutions dual to $d$-dimensional field theories at finite charge density have a near-horizon region, which is ${\mathrm{AdS}}_{2}\ifmmode\times\else\texttimes\fi{}{\mathbb{R}}^{d\ensuremath{-}1}$. The scale invariance of the ${\mathrm{AdS}}_{2}$ region implies that at low energies the dual field theory exhibits emergent quantum critical behavior controlled by a ($0+1$)-dimensional conformal field theories (CFT). This interpretation sheds light on recently-discovered holographic descriptions of Fermi surfaces, allowing an analytic understanding of their low-energy excitations. For example, the scaling behavior near the Fermi surfaces is determined by conformal dimensions in the emergent IR CFT. In particular, when the operator is marginal in the IR CFT, the corresponding spectral function is precisely of the ``marginal Fermi liquid'' form, postulated to describe the optimally doped cuprates.

An AdS_3 Dual for Minimal Model CFTs

Abstract: We propose a duality between the 2d ${\mathcal{W}}_{N}$ minimal models in the large $N$ 't Hooft limit, and a family of higher spin theories on ${\mathrm{AdS}}_{3}$. The 2d conformal field theories (CFTs) can be described as Wess-Zumino-Witten coset models, and include, for $N=2$, the usual Virasoro unitary series. The dual bulk theory contains, in addition to the massless higher spin fields, two complex scalars (of equal mass). The mass is directly related to the 't Hooft coupling constant of the dual CFT. We give convincing evidence that the spectra of the two theories match precisely for all values of the 't Hooft coupling. We also show that the renormalization group flows in the 2d CFT agree exactly with the usual AdS/CFT prediction of the gravity theory. Our proposal is in many ways analogous to the Klebanov-Polyakov conjecture for an ${\mathrm{AdS}}_{4}$ dual for the singlet sector of large $N$ vector models.

Non-Fermi liquids from holography

Abstract: We report on a potentially new class of non-Fermi liquids in (2+1)-dimensions. They are identified via the response functions of composite fermionic operators in a class of strongly interacting quantum field theories at finite density, computed using the AdS/CFT correspondence. We find strong evidence of Fermi surfaces: gapless fermionic excitations at discrete shells in momentum space. The spectral weight exhibits novel phenomena, including particle-hole asymmetry, discrete scale invariance, and scaling behavior consistent with that of a critical Fermi surface postulated by Senthil.

Writing CFT correlation functions as AdS scattering amplitudes

Abstract: We explore the Mellin representation of conformal correlation functions recently proposed by Mack. Examples in the AdS/CFT context reinforce the analogy between Mellin amplitudes and scattering amplitudes. We conjecture a simple formula relating the bulk scattering amplitudes to the asymptotic behavior of Mellin amplitudes and show that previous results on the flat space limit of AdS follow from our new formula. We find that the Mellin amplitudes are particularly useful in the case of conformal gauge theories in the planar limit. In this case, the four point Mellin amplitudes are meromorphic functions whose poles and their residues are entirely determined by two and three point functions of single-trace operators. This makes the Mellin amplitudes the ideal objects to attempt the conformal bootstrap program in higher dimensions.

Spinning conformal correlators

Abstract: We develop the embedding formalism for conformal field theories, aimed at doing computations with symmetric traceless operators of arbitrary spin. We use an index-free notation where tensors are encoded by polynomials in auxiliary polarization vectors. The efficiency of the formalism is demonstrated by computing the tensor structures allowed in n-point conformal correlation functions of tensors operators. Constraints due to tensor conservation also take a simple form in this formalism. Finally, we obtain a perfect match between the number of independent tensor structures of conformal correlators in d dimensions and the number of independent structures in scattering amplitudes of spinning particles in (d+1)-dimensional Minkowski space.

Towards the F-theorem: $ \mathcal{N} = 2 $ field theories on the three-sphere

Abstract: For 3-dimensional field theories with $ \mathcal{N} = 2 $ supersymmetry the Euclidean path integrals on the three-sphere can be calculated using the method of localization; they reduce to certain matrix integrals that depend on the R-charges of the matter fields. We solve a number ofsuch large N matrix models and calculate the free energy F as a function of the trial R-charges consistent with the marginality of the super potential. In all our $ \mathcal{N} = 2 $ superconformal examples, the local maximization of F yields answers that scale as N 3/2 and agree with the dual M-theory backgrounds AdS 4 × Y, where Y are 7-dimensional Sasaki-Einstein spaces. We also find in toric examples that local F-maximization is equivalent to the minimization of the volume of Y over the space of Sasakian metrics, a procedure also referred to as Z-minimization. Moreover, we find that the functions F and Z are related for any trial R-charges. In the models we study F is positive and decreases along RG flows. We therefore propose the “F-theorem” that we hope applies to all 3-d field theories: the finite part of the free energy on the three-sphere decreases along RG trajectories and is stationary at RG fixed points. We also show that in an infinite class of Chern-Simons-matter gauge theories where the Chern-Simons levels do not sum to zero, the free energy grows as N 5/3 at large N. This non-trivial scaling matches that of the free energy of the gravity duals in type IIA string theory with Romans mass.

On graviton non-gaussianities during inflation

Abstract: We consider the most general three point function for gravitational waves produced during a period of exactly de Sitter expansion. The de Sitter isometries constrain the possible shapes to only three: two preserving parity and one violating parity. These isometries imply that these correlation functions should be conformal invariant. One of the shapes is produced by the ordinary gravity action. The other shape is produced by a higher derivative correction and could be as large as the gravity contribution. The parity violating shape does not contribute to the bispectrum (1, 2), even though it is present in the wavefunction. We also introduce a spinor helicity formalism to describe de Sitter gravitational waves with circular polarization. These results also apply to correlation functions in Anti-de Sitter space. They also describe the general form of stress tensor correlation functions, in momentum space, in a three dimensional conformal field theory. Here all three shapes can arise, including the parity violating one.

Hydrodynamics from charged black branes

Abstract: We extend the recent work on fluid-gravity correspondence to charged black-branes by determining the metric duals to arbitrary charged fluid configuration up to second order in the boundary derivative expansion. We also derive the energy-momentum tensor and the charge current for these configurations up to second order in the boundary derivative expansion. We find a new term in the charge current when there is a bulk Chern-Simons interaction thus resolving an earlier discrepancy between thermodynamics of charged rotating black holes and boundary hydrodynamics. We have also confirmed that all our expressions are covariant under boundary Weyl-transformations as expected.

Holographic Dual of a Boundary Conformal Field Theory

Abstract: We propose a holographic dual of a conformal field theory defined on a manifold with boundaries, i.e., boundary conformal field theory (BCFT). Our new holography, which may be called anti-de Sitter BCFT, successfully calculates the boundary entropy or g function in two-dimensional BCFTs and it agrees with the finite part of the holographic entanglement entropy. Moreover, we can naturally derive a holographic g theorem. We also analyze the holographic dual of an interval at finite temperature and show that there is a first order phase transition.

Holographic and Wilsonian renormalization groups

Abstract: We develop parallels between the holographic renormalization group in the bulk and the Wilsonian renormalization group in the dual field theory. Our philosophy differs from most previous work on the holographic RG; the most notable feature is the key role of multi-trace operators. We work out the forms of various single-and double-trace flows. The key question, ‘what cutoff on the field theory corresponds to a radial cutoff in the bulk?’ is left unanswered, but by sharpening the analogy between the two sides we identify possible directions.

Thermalization of strongly coupled field theories

Abstract: Using the holographic mapping to a gravity dual, we calculate 2-point functions, Wilson loops, and entanglement entropy in strongly coupled field theories in d=2, 3, and 4 to probe the scale dependence of thermalization following a sudden injection of energy. For homogeneous initial conditions, the entanglement entropy thermalizes slowest and sets a time scale for equilibration that saturates a causality bound. The growth rate of entanglement entropy density is nearly volume-independent for small volumes but slows for larger volumes. In this setting, the UV thermalizes first.

Generalized Holographic Quantum Criticality at Finite Density

Abstract: We show that the near-extremal solutions of Einstein-Maxwell-Dilaton theories, studied in ArXiv:1005.4690, provide IR quantum critical geometries, by embedding classes of them in higher-dimensional AdS and Lifshitz solutions. This explains the scaling of their thermodynamic functions and their IR transport coefficients, the nature of their spectra, the Gubser bound, and regulates their singularities. We propose that these are the most general quantum critical IR asymptotics at finite density of EMD theories.

On holographic entanglement entropy and higher curvature gravity

Abstract: We examine holographic entanglement entropy with higher curvature gravity in the bulk. We show that in general Wald’s formula for horizon entropy does not yield the correct entanglement entropy. However, for Lovelock gravity, there is an alternate prescription which involves only the intrinsic curvature of the bulk surface. We verify that this prescription correctly reproduces the universal contribution to the entanglement entropy for CFT’s in four and six dimensions. We also make further comments on gravitational theories with more general higher curvature interactions.

A natural language for AdS/CFT correlators

Abstract: We provide dramatic evidence that ‘Mellin space’ is the natural home for correlation functions in CFTs with weakly coupled bulk duals. In Mellin space, CFT correlators have poles corresponding to an OPE decomposition into ‘left’ and ‘right’ sub-correlators, in direct analogy with the factorization channels of scattering amplitudes. In the regime where these correlators can be computed by tree level Witten diagrams in AdS, we derive an explicit formula for the residues of Mellin amplitudes at the corresponding factorization poles, and we use the conformal Casimir to show that these amplitudes obey algebraic finite difference equations. By analyzing the recursive structure of our factorization formula we obtain simple diagrammatic rules for the construction of Mellin amplitudes corresponding to tree-level Witten diagrams in any bulk scalar theory. We prove the diagrammatic rules using our finite difference equations. Finally, we show that our factorization formula and our diagrammatic rules morph into the flat space S-Matrix of the bulk theory, reproducing the usual Feynman rules, when we take the flat space limit of AdS/CFT. Throughout we emphasize a deep analogy with the properties of flat space scattering amplitudes in momentum space, which suggests that the Mellin amplitude may provide a holographic definition of the flat space S-Matrix.

Index for three dimensional superconformal field theories with general R-charge assignments

Abstract: We derive a general formula of an index for three dimensional \( \mathcal{N} = 2 \) super-conformal field theories with general R-charge assignments to chiral multiplets by using the localization method in S2 × S1 background. As examples we compute the index for theories in a few mirror pairs, and confirm the agreement of the indices in each mirror pair.

Integrating out geometry : holographic Wilsonian RG and the membrane paradigm.

Abstract: We formulate a holographic Wilsonian renormalization group flow for strongly coupled systems with a gravity dual, motivated by the need to extract efficiently low energy behavior of such systems. Starting with field theories defined on a cut-off surface in a bulk spacetime, we propose that integrating out high energy modes in the field theory should correspond to integrating out a part of the bulk geometry. We describe how to carry out this procedure in practice in the classical gravity approximation using examples of scalar and vector fields. By integrating out bulk degrees of freedom all the way to a black hole horizon, this formulation defines a refined version of the black hole membrane paradigm. Furthermore, it also provides a derivation of the semi-holographic description of low energy physics.

Symmetries of Holographic Minimal Models

Abstract: It was recently proposed that a large N limit of a family of minimal model CFTs is dual to a certain higher spin gravity theory in AdS3, where the ’t Hooft coupling constant of the CFT is related to a deformation parameter of the higher spin algebra. We identify the asymptotic symmetry algebra of the higher spin theory for generic ’t Hooft parameter, and show that it coincides with a family of $ \mathcal{W} $ -algebras previously discovered in the context of the KP hierarchy. We furthermore demonstrate that this family of $ \mathcal{W} $ -algebras controls the representation theory of the minimal model CFTs in the ’t Hooft limit. This provides a non-trivial consistency check of the proposal and explains part of the underlying mechanism.

Bounds on 4D conformal and superconformal field theories

Abstract: We derive general bounds on operator dimensions, central charges, and OPE coefficients in 4D conformal and $ \mathcal{N} = 1 $ superconformal field theories. In any CFT containing a scalar primary ϕ of dimension d we show that crossing symmetry of $ \left\langle {\phi \phi \phi \phi } \right\rangle $ implies a completely general lower bound on the central charge c ≥ f c (d). Similarly, in CFTs containing a complex scalar charged under global symmetries, we bound a combination of symmetry current two-point function coefficients τ IJ and flavor charges. We extend these bounds to $ \mathcal{N} = 1 $ superconformal theories by deriving the superconformal block expansions for four-point functions of a chiral superfield Φ and its conjugate. In this case we derive bounds on the OPE coefficients of scalar operators appearing in the Φ × Φ† OPE, and show that there is an upper bound on the dimension of Φ†Φ when dim Φ is close to 1. We also present even more stringent bounds on c and τ IJ . In supersymmetric gauge theories believed to flow to superconformal fixed points one can use anomaly matching to explicitly check whether these bounds are satisfied.

Higher Spin Black Holes

Abstract: We study classical solutions of three dimensional higher spin gravity in the Chern-Simons formulation. We find solutions that generalize the BTZ black hole and carry spin-3 charge. The black hole entropy formula yields a result for the asymptotic growth of the partition function at finite spin-3 chemical potential. Along the way, we develop technology for computing AdS/CFT correlation functions involving higher spin operators.

An operator product expansion for polygonal null Wilson loops

Abstract: We consider polygonal Wilson loops with null edges in conformal gauge theories. We derive an OPE-like expansion when several successive lines of the polygon are becoming aligned. The limit corresponds to a collinear, or multicollinear, limit and we explain the systematics of all the subleading corrections, going beyond the leading terms that were previously considered. These subleading corrections are governed by excitations of high spin operators, or excitations of a flux tube that goes between two Wilson lines. The discussion is valid for any conformal gauge theory, for any coupling and in any dimension.

Higher spins in AdS and twistorial holography

Abstract: In this paper we simplify and extend previous work on three-point functions in Vasiliev’s higher spin gauge theory in AdS4. We work in a gauge in which the space-time dependence of Vasiliev’s master fields is gauged away completely, leaving only the internal twistor-like variables. The correlation functions of boundary operators can be easily computed in this gauge. We find complete agreement of the tree level three point functions of higher spin currents in Vasiliev’s theory with the conjectured dual free O(N) vector theory.

Constructing local bulk observables in interacting AdS/CFT

Abstract: Local operators in the bulk of anti-de Sitter can be represented as smeared operators in the dual conformal field theory. We show how to construct these bulk observables by requiring that the bulk operators commute at spacelike separation. This extends our previous work by taking interactions into account. Large-N factorization plays a key role in the construction. We show diagrammatically how this procedure is related to bulk Feynman diagrams.

Towards Feynman rules for Mellin amplitudes in AdS/CFT

Abstract: We investigate the use of the embedding formalism and the Mellin transform in the calculation of tree-level conformal correlation functions in AdS/CFT. We evaluate 5- and 6-point Mellin amplitudes in 3 theory and even a 12-pt diagram in 4 theory, enabling us to conjecture a set of Feynman rules for scalar Mellin amplitudes. The general vertices are given in terms of Lauricella generalized hypergeometric functions. We also show how to use the same combination of Mellin transform and embedding formalism for amplitudes involving elds with spin. The complicated tensor structures which usually arise can be written as certain operators acting as projectors on much simpler index structures - essentially the same ones appearing in a at space amplitude. Using these methods we are able to evaluate a four-point current diagram with current exchange in Yang-Mills theory.

T-systems and Y-systems in integrable systems*

Abstract: T- and Y-systems are ubiquitous structures in classical and quantum integrable systems. They are difference equations having a variety of aspects related to commuting transfer matrices in solvable lattice models, q-characters of Kirillov–Reshetikhin modules of quantum affine algebras, cluster algebras with coefficients, periodicity conjectures of Zamolodchikov and others, dilogarithm identities in conformal field theory, difference analog of L-operators in KP hierarchy, Stokes phenomena in 1D Schrodinger problem, AdS/CFT correspondence, Toda field equations on discrete spacetime, Laplace sequence in discrete geometry, Fermionic character formulas and combinatorial completeness of Bethe ansatz, Q-system and ideal gas with exclusion statistics, analytic and thermodynamic Bethe ansatze, quantum transfer matrix method and so forth. This review is a collection of short reviews on these topics which can be read more or less independently.

Aspects of AdS/BCFT

Abstract: We expand the results of arXiv:1105.5165, where a holographic description of a conformal field theory defined on a manifold with boundaries (so called BCFT) was proposed, based on AdS/CFT. We construct gravity duals of conformal field theories on strips, balls and also time-dependent boundaries. We show a holographic g-theorem in any dimension. As a special example, we can define a ‘boundary central charge’ in three dimensional conformal field theories and our holographic g-theorem argues that it decreases under RG flows. We also computed holographic one-point functions and confirmed that their scaling property agrees with field theory calculations. Finally, we give an example of string theory embedding of this holography by inserting orientifold 8-planes in AdS4 × CP3.

Wilsonian Approach to Fluid/Gravity Duality

Abstract: The problem of gravitational fluctuations confined inside a finite cutoff at radius r = r c outside the horizon in a general class of black hole geometries is considered. Consistent boundary conditions at both the cutoff surface and the horizon are found and the resulting modes analyzed. For general cutoff r c the dispersion relation is shown at long wavelengths to be that of a linearized Navier-Stokes fluid living on the cutoff surface. A cutoff-dependent line-integral formula for the diffusion constant D (r c ) is derived. The dependence on r c is interpreted as renormalization group (RG) flow in the fluid. Taking the cutoff to infinity in an asymptotically AdS context, the formula for D(∞) reproduces as a special case well-known results derived using AdS/CFT. Taking the cutoff to the horizon, the effective speed of sound goes to infinity, the fluid becomes incompressible and the Navier-Stokes dispersion relation becomes exact. The resulting universal formula for the diffusion constant D(horizon) reproduces old results from the membrane paradigm. Hence the old membrane paradigm results and new AdS/CFT results are related by RG flow. RG flow-invariance of the viscosity to entropy ratio $ \frac{\eta }{s} $ is shown to follow from the first law of thermodynamics together with isentropy of radial evolution in classical gravity. The ratio is expected to run when quantum gravitational corrections are included.

Effective conformal theory and the flat-space limit of AdS

Abstract: We develop the idea of an effective conformal theory describing the low-lying spectrum of the dilatation operator in a CFT. Such an effective theory is useful when the spectrum contains a hierarchy in the dimension of operators, and a small parameter whose role is similar to that of 1/N in a large N gauge theory. These criteria insure that there is a regime where the dilatation operator is modified perturbatively. Global AdS is the natural framework for perturbations of the dilatation operator respecting conformal invariance, much as Minkowski space naturally describes Lorentz invariant perturbations of the Hamiltonian. Assuming that the lowest-dimension single-trace operator is a scalar, $ \mathcal{O} $ , we consider the anomalous dimensions, γ(n, l), of the double-trace operators of the form $ \mathcal{O}{\left( {{\partial^2}} \right)^n}{\left( \partial \right)^l}\mathcal{O} $ . Purely from the CFT we find that perturbative unitarity places a bound on these dimensions of |γ(n, l)| < 4. Non-renormalizable AdS interactions lead to violations of the bound at large values of n. We also consider the case that these interactions are generated by integrating out a heavy scalar field in AdS. We show that the presence of the heavy field “unitarizes” the growth in the anomalous dimensions, and leads to a resonance-like behavior in γ(n, l) when n is close to the dimension of the CFT operator dual to the heavy field. Finally, we demonstrate that bulk flat-space S-matrix elements can be extracted from the large n behavior of the anomalous dimensions. This leads to a direct connection between the spectrum ofanomalous dimensions in d-dimensional CFTs and flat-space S-matrix elements in d + 1 dimensions. We comment on the emergence of flat-space locality from the CFT perspective.

Nonperturbative aspects of ABJM theory

Abstract: Using the matrix model which calculates the exact free energy of ABJM theory on $ {\mathbb{S}^3} $ we study non-perturbative effects in the large N expansion of this model, i.e., in the genus expansion of type IIA string theory on AdS4 × $ \mathbb{C}{\mathbb{P}^3} $ . We propose a general prescription to extract spacetime instanton actions from general matrix models, in terms of period integrals of the spectral curve, and we use it to determine them explicitly in the ABJM matrix model, as exact functions of the ’t Hooft coupling. We confirm numerically that these instantons control the asymptotic growth of the genus expansion. Furthermore, we find that the dominant instanton action at strong coupling determined in this way exactly matches the action of an Euclidean D2-brane instanton wrapping $ \mathbb{R}{\mathbb{P}^3} $ .